Hi, I'm new on this site and I thought I'd give it a shot. I'm have problems approximating real zeros of f(x)=0.25x^3-7x^2+15
My book doesn't give very good examples and I'm pretty much lost, can someone please help me?

This one is a booger because it's roots are not nice integers or rationals.

One thing to do is get a calculator and use the Intermediate Value Theorem.

For instance, if you enter a value and get a positive result, then enter a value and get

a negative result, the root is in between those two values.


Here's one:

Try 1 in the equation and you get 33

Try 2 and you get -44

Therefore, a root is between 1 and 2.

Keep closing in on it. Try 1.5 you get 0.375

Try 1.6 and you get -7.584.

So, it's between 1.5 and 1.6.

Keeping this up until we get as close as we need to be satisfied.

The root is 1.50484722289. Round off where you wish.

Try to find the other two. I will tell you to try between the values 27 and 28 for one and

-1 and -2 for the other.

Good luck